Quote "We have not the slightest idea of what this equation means, but we may be certain that it means something very important" This is why we love this stuff! That quote to my mind, sums up the mystery and excitement of the pursuit of knowledge. Superb quote.
Euler discovered the identity 158^4 = 134^4 + 133^4 - 59^4 . Checking it out on my calculator from memory I input 159^4 -134^4 -133^4 = 3810304 which is 1952^2. Removing the two common terms from both equations gives 159^4 = 158^4 +59^4 +1952^2. So there you have it, a trio of interrelated quadruples I have called Euler - Bateman quadruples. They are in fact Pythagorean quadruples. Many similarly related trios are also found in cubic quadruples. At the time I had this strange feeling that Euler was whispering in my ear but alas I didn't know what he was saying as I can't speak German. An excellent lecture that was easy to follow and listen to.
About that Irish Coffee question: the trick to keeping the cup/glass warm the longest is to WHIP the cream just enough to incorporate air at 20-25% by volume, and let the cream integrate slowly into the coffee as its whipping fails. While it still sits atop the coffee with air emulsified in it, the cream will greatly slow heat loss from the entire top surface of the coffee. :-)
Sound tech speaking: most of that's not the fault of the professor's voice, but of the technician's over-reaction to its natural variations (the clue is how drastically the room's reverb varies with the overall level of volume). Rather than working volume changes in gently and in tiny increments to keep the "average" tracking smoothly, the tech far too often waits until excess/insufficient volume gets really hard for even casual listeners to ignore.
"... one of histories greatest mathematicians" should read "... one of history's greatest mathematicians" or rather "... history's greatest mathematician".
